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• VCMSP300

  Investigate the effect of individual data values including outliers, on the range, mean and median

  Elaborations

  • using displays of data to explore and investigate effects
  • exploring the effect of outliers on the range for different sets of data by comparing its value with and without outliers included

  VCMSP300 | Mathematics | Level 8 | Statistics and Probability | Data representation and interpretation

• VC2M8ST01

  distinguish between a population and a sample, and investigate techniques for data collection including census, sampling, experiment and observation, and explain the practicalities and implications of obtaining data through these techniques

  Elaborations

  • identifying situations where data can be collected by census and those where a sample is appropriate
  • investigating the practicalities and implications of obtaining data through sampling, using a variety of investigative processes; for example, investigating situations when random sampling or non-random sampling is used to collect data and the implication of each sampling method
  • discussing how observations, experiments and sampling methods can be impacted by bias; for example, recognising that a sampling bias occurs when certain members of a population are more likely to be selected in a sample than others, such as a survey conducted at a shopping centre, and recognising that environmental conditions may bias the results of scientific investigations if experiments are conducted at different times or under different conditions
  • using digital tools such as simulations and digital measuring devices to observe, measure and record qualitative and quantitative data, discussing precision and the implications of error

  VC2M8ST01 | Mathematics | Mathematics Version 2.0 | Level 8 | Statistics

• VC2M8M03

  solve problems involving the circumference and area of a circle using formulas and appropriate units

  Elaborations

  • deducing that the area of a circle is between 2 radius squares and 4 radius squares, and using 3 × radius² as a rough estimate for the area of a circle
  • investigating the area of circles using a square grid or by rearranging a circle divided into smaller and smaller sectors or slices to resemble a close approximation of a rectangle
  • applying the formulas for the area and circumference of a circle to solve practical problems, and using one of the measures of radius, diameter, circumference or area to deduce the value of the other measures; for example, determining the length of material needed to edge a round table, given its dimensions as the area of the tabletop
  • exploring traditional weaving designs by Aboriginal and Torres Strait Islander Peoples and investigating the significance and use of circles

  VC2M8M03 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• VC2M8A03

  use mathematical modelling to solve applied problems involving linear relations, including financial contexts involving profit and loss; formulate problems with linear functions, and choose a representation; interpret and communicate solutions in terms of the context, and review the appropriateness...

  Elaborations

  • modelling situations involving linear functions, including practical contexts such as taxi fares involving flag fall fees, motion in a straight line at a constant speed, trade quotes involving call-out fees, cooking that includes resting or cooling times, or water leakage from water tanks, interpreting the constant rate of change and initial value in context, and identifying when values of a model lie within a given range
  • modelling problems in practical situations and interpreting solutions within the context of the problem, including giving attention to all units of measure and whether results are suitable; for example, once a water tank is empty no more water can flow from it
  • modelling financial problems involving pay rates, using a table of values to represent the pay amounts and hours worked using an hourly rate of pay, and graphing the relationship to make inferences
  • modelling patterns on Country/Place and exploring their connections and meaning to linear equations, using the model as a predictive tool and critiquing results by connecting back to Country/Place

  VC2M8A03 | Mathematics | Mathematics Version 2.0 | Level 8 | Algebra

• VCMMG292

  Develop the conditions for congruence of triangles

  Elaborations

  • investigating the minimal conditions needed for the unique construction of triangles, leading to the establishment of the conditions for congruence (SSS, SAS, ASA and RHS)
  • solving problems using the properties of congruent figures
  • constructing triangles using the conditions for congruence

  VCMMG292 | Mathematics | Level 8 | Measurement and Geometry | Geometric reasoning

• VCMNA283

  Plot linear relationships on the Cartesian plane with and without the use of digital technologies

  Elaborations

  • completing a table of values, plotting the resulting points and determining whether the relationship is linear
  • finding the rule for a linear relationship

  VCMNA283 | Mathematics | Level 8 | Number and Algebra | Linear and non-linear relationships

• VC2M8M01

  solve problems involving the area and perimeter of irregular and composite shapes using appropriate units

  Elaborations

  • determining the area of composite shapes by composing or decomposing shapes
  • using arrays and rectangles to approximate the area of irregular shapes in situations such as a council needing to work out how much mosquito spray to use for a swamp area or a farmer needing to work out how much seed, fertiliser and herbicide are required to cover a paddock
  • determining the perimeter and area of irregular shapes by sums of increasingly accurate covering measurements, such as line segments and grids; for example, using millimetres or square millimetres as opposed to centimetres or square centimetres

  VC2M8M01 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• VCMNA281

  Simplify algebraic expressions involving the four operations

  Elaborations

  • understanding that the laws used with numbers can also be used with algebra

  VCMNA281 | Mathematics | Level 8 | Number and Algebra | Patterns and algebra

• VC2M8N05

  solve problems involving the use of percentages, including percentage increases and decreases and percentage error, with and without digital tools

  Elaborations

  • using percentages to solve problems, including those involving mark-ups, discounts and Goods and Services Tax (GST)
  • using percentages to calculate population increases and decreases
  • using percentage error to compare the relative size of error in calculations involving a given or actual value, and an estimated or measured value

  VC2M8N05 | Mathematics | Mathematics Version 2.0 | Level 8 | Number

• VCMNA276

  Solve problems involving the use of percentages, including percentage increases and decreases and percentage error, with and without digital technologies

  Elaborations

  • using percentages to solve problems, including those involving mark-ups, discounts, and GST
  • using percentages to calculate population increases and decreases
  • using percentage error to compare relative size of error in calculations involving a given or actual value, and an estimated or measured value

  VCMNA276 | Mathematics | Level 8 | Number and Algebra | Real numbers

• VCMNA285

  Plot graphs of non-linear real life data with and without the use of digital technologies, and interpret and analyse these graphs

  Elaborations

  • investigating different combinations of length and width of a rectangle for a fixed area, and drawing the corresponding graph
  • using graphs to analysing change in the value of a currency against another currency over a specified period

  VCMNA285 | Mathematics | Level 8 | Number and Algebra | Linear and non-linear relationships

• VC2M8M06

  use Pythagoras’ theorem to solve problems involving the side lengths of right-angled triangles

  Elaborations

  • discussing and comparing different applications, demonstrations and proofs of Pythagoras’ theorem, from Egypt and Mesopotamia, Greece, India and China, with other historical and contemporary applications and proofs
  • using Pythagoras’ theorem to determine unknown lengths of sides in right-angled triangles and finding lengths of sides of right-angled triangles in practical applications
  • recognising the relationship between the squares of lengths of sides for different types of triangles: right-angled, acute or obtuse
  • identifying Pythagorean triples, such as (3, 4, 5), (5, 12, 13), (7, 24, 25) and (8, 15, 17)

  VC2M8M06 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• VCMSP297

  Distinguish between a population and a sample and investigate techniques for collecting data, including census, sampling and observation

  Elaborations

  • identifying situations where data can be collected by census and those where a sample is appropriate
  • investigating the differences between convenience, judgemental and simple random sampling from a population

  VCMSP297 | Mathematics | Level 8 | Statistics and Probability | Data representation and interpretation

• VC2M8N02

  establish and apply the exponent laws with positive integer exponents and the zero exponent, using exponent notation with numbers

  Elaborations

  • recognising the connection between exponent form and expanded form with the exponent laws of product of powers rule, quotient of powers rule, and power of a power rule, for example, 23×22 can be represented as 2×2×2×2×2=25 , and connecting the result to the addition of exponents
  • applying the exponent laws of the product of powers rule, quotient of powers rule, power of a power rule and zero exponent individually and in combination; for example, using exponents to determine the effect on the volume of a 2 centimetre cube when the cube is enlarged to a 6 centimetre cube, 6323= 23×3323=33, so the volume is increased by a factor of 27
  • using digital tools to systematically explore the application of the exponent laws; observing that the bases need to be the same
  • using examples such as 3434=1, and 34-4=30 to illustrate the necessity that for any non-zero natural number n,  n0=1

  VC2M8N02 | Mathematics | Mathematics Version 2.0 | Level 8 | Number

• VCMNA277

  Solve a range of problems involving rates and ratios, including distance-time problems for travel at a constant speed, with and without digital technologies

  Elaborations

  • understanding that rate and ratio problems can be solved using fractions or percentages and choosing the most efficient form to solve a particular problem
  • calculating population growth rates in Australia and Asia and explaining their difference
  • finding one of distance travelled, time taken or average speed given the other two quantities

  VCMNA277 | Mathematics | Level 8 | Number and Algebra | Real numbers

• VC2M8N04

  use the 4 operations with integers and with rational numbers, choosing and using efficient mental and written strategies, and digital tools where appropriate, and making estimates for these computations

  Elaborations

  • using patterns to assist in establishing the rules for the multiplication and division of integers
  • applying and explaining efficient strategies such as using the commutative or associative property for regrouping, partitioning, place value, patterning, multiplication or division facts to solve problems involving positive and negative integers, fractions and decimals
  • recognising the effect of sign in the multiplication of integers, for example, (-1)4=1 and (-1)5=-1

  VC2M8N04 | Mathematics | Mathematics Version 2.0 | Level 8 | Number

• VC2M8M02

  solve problems involving the volume and capacity of right prisms using appropriate units

  Elaborations

  • using models to demonstrate the number of cubic centimetres in a cubic metre and relating this to capacities of millilitres and litres, recognising that one millilitre is equivalent to one cm³
  • solving practical problems involving volume and capacity, for example, optimal packaging and production
  • choosing which measurements are useful to consider when solving practical problems in context; for example, when purchasing a new washing machine, the dimensions are useful when determining whether it will fit in the available space in the laundry and its capacity is useful when considering the maximum washing load it can carry
  • investigating, reasoning and finding solutions to measurement problems involving dimensions, rates, volume and capacity of objects; for example, given the dimensions of a pool and the rate of flow from a tap, determining how long it will take to fill the pool to its normal capacity

  VC2M8M02 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• VC2M8A02

  graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution

  Elaborations

  • recognising that in a table of values, if the first difference between consecutive values of the dependent variable is constant, then it is a linear relation
  • graphing linear functions and relations of the form x=a , y=a , x ≤a , x>a , y ≤a , y>a on the Cartesian plane for known values of a
  • completing a table of values, plotting the resulting points on the Cartesian plane and determining whether the relationship is linear
  • graphing the linear relationship ax+b=c for given values of a, b and c and identifying from the graph where ax+b <c or where ax+b >c
  • solving linear equations of the form ax+b=c and one-variable inequalities of the form ax+b <c or ax+b >c where a > 0 using inverse operations and digital tools, and checking solutions by substitution
  • solving linear equations such as 3x+7=6x-9 , representing these graphically, and verifying solutions by substitution

  VC2M8A02 | Mathematics | Mathematics Version 2.0 | Level 8 | Algebra